How to perfectly position these faces into this slot / area? (no gaps)
Your best bet is to use the snapping tools, specifically the vertex snapping mode, as others have said in the comments. The snapping tools take a little getting used to, but are really quite powerful. As I have noticed when using vertex snapping, Blender seems to take one vertex from your selection and try to snap it to the positions of others not in your selection while all other selected verts move in relation to the snapping vertex. Unfortunately I don't think you can specify which vertex will do the snapping, not exactly. You can however almost always change how the surfaces will attempt to snap together by moving the objects in relation to each other before hand.

The key is first placing your object so it can find a good snap, then moving it with snap mode. Using the ctrl key is really helpful for this.

For example:
If you are trying to snap cube A to above cube B, but cube A is somewhere off to the right side of cube B, Blender will only want to snap cube A on to the left side of cube B. However if you first move cube A somewhere above cube B, you should be able to snap cube A down onto the top of cube B.